%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET917+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:57:48 AM UTC 2026
% Result : Theorem 0.14s 10.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(l28_zfmisc_1,axiom,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_zfmisc_1) ).
fof(l32_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('theBenchmark.p',l32_zfmisc_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t58_zfmisc_1,conjecture,
! [A,B] :
( set_intersection2(singleton(A),B) = singleton(A)
| disjoint(singleton(A),B) ),
file('theBenchmark.p',t58_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] : set_intersection2(U_3,U_2) = set_intersection2(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
set_intersection2(U_3,U_2) = set_intersection2(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_3_2,plain,
! [U_5,U_4] : set_intersection2(U_5,U_5) = U_5,
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_5] : set_intersection2(U_5,U_5) = U_5,
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
set_intersection2(U_5,U_5) = U_5,
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_4_2,plain,
! [U_7,U_6] :
( disjoint(singleton(U_7),U_6)
| in(U_7,U_6) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( disjoint(singleton(U_7),U_6)
| in(U_7,U_6) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] :
( set_intersection2(B,singleton(A)) = singleton(A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l32_zfmisc_1]) ).
fof(f_5_2,plain,
! [U_9,U_8] :
( set_intersection2(U_8,singleton(U_9)) = singleton(U_9)
| ~ in(U_9,U_8) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( set_intersection2(U_8,singleton(U_9)) = singleton(U_9)
| ~ in(U_9,U_8) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_6_2,plain,
? [U_10] : empty(U_10),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1)],[f_6_2]) ).
cnf(f_6_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_7_2,plain,
? [U_11] : ~ empty(U_11),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_11,sK2)],[f_7_2]) ).
cnf(f_7_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_8_2,plain,
! [U_13,U_12] :
( disjoint(U_12,U_13)
| ~ disjoint(U_13,U_12) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( disjoint(U_12,U_13)
| ~ disjoint(U_13,U_12) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,negated_conjecture,
~ ! [A,B] :
( set_intersection2(singleton(A),B) = singleton(A)
| disjoint(singleton(A),B) ),
inference(negate,[status(cth)],[t58_zfmisc_1]) ).
fof(f_9_2,negated_conjecture,
? [A,B] :
( set_intersection2(singleton(A),B) != singleton(A)
& ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_15,U_14] :
( set_intersection2(singleton(U_15),U_14) != singleton(U_15)
& ~ disjoint(singleton(U_15),U_14) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_14] :
( set_intersection2(singleton(sK3),U_14) != singleton(sK3)
& ~ disjoint(singleton(sK3),U_14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_15,sK3)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
( set_intersection2(singleton(sK3),sK4) != singleton(sK3)
& ~ disjoint(singleton(sK3),sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_14,sK4)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( set_intersection2(singleton(sK3),sK4) != singleton(sK3)
& ~ disjoint(singleton(sK3),sK4) ),
inference(definitional_conversion,[status(esa)],[f_9_5]) ).
cnf(f_9_7,negated_conjecture,
~ disjoint(singleton(sK3),sK4),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(f_9_8,negated_conjecture,
set_intersection2(singleton(sK3),sK4) != singleton(sK3),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_7,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_8,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET917+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.37 % Computer : n008.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Sat Sep 19 23:08:21 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.14/10.41 % SZS status Theorem for theBenchmark
% 0.14/10.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------